Identification method for a fractional-order system in terms of equivalent dynamic properties.

In this paper, we introduce an efficient method for identifying fractional dynamic systems using extended sparse regression and cross-validation techniques. The former identifies equations that fit the data with varying candidate functions, while the latter determines the optimal equation with the fewest terms yet ensuring accuracy. The identified optimal equation is expected to share the same dynamic properties as the original fractional system.

Sparse identification of nonlinear dynamical systems via non-convex penalty least squares.

This paper proposes a non-convex penalty regression method to identify governing equations of nonlinear dynamical systems from noisy state measurements. The idea to connect the non-convex penalty function instead of the l - norm with least squares is due to the fact that the l - norm excessively penalizes large coefficients and may incur estimation bias. The purpose of this work is to improve the accuracy and robustness in regression tasks.

An improved cell mapping method based on dimension-extension for fractional systems.

Global analysis of fractional systems is a challenging topic due to the memory property. Without the Markov assumption, the cell mapping method cannot be directly applied to investigate the global dynamics of such systems. In this paper, an improved cell mapping method based on dimension-extension is developed to study the global dynamics of fractional systems.